Question

A basketball player shoots a ball towards the hoop. The trajectory of the ball can be modeled by the quadratic functionf(x) = −(x+1.4)2+6 , where x represents the horizontal distance in feet from the player, and f(x) represents the height of the ball in feet. (1 point) Part A: Identify the vertex (write your answer as an ordered pair): Part B: Complete the table x f(x) 0 1 2 3 Skip to navigation

Answer 1

To analyze the quadratic function \( f(x) = -(x + 1.4)^2 + 6 \), we can break down the two parts you've mentioned.

### Part A: Identify the vertex
The vertex form of a quadratic function is given by \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. In this case, the function is given as:

\[
f(x) = -(x + 1.4)^2 + 6
\]

We can rewrite this in vertex form:

1. The vertex is found directly from the expression \( -(x + 1.4)^2 + 6 \).
2. Here, \( h = -1.4 \) and \( k = 6 \).

Thus, the vertex is:

\[
\text{Vertex} = (-1.4, 6)
\]

### Part B: Complete the table
Now we'll calculate \( f(x) \) for the given values \( x = 0, 1, 2, \) and \( 3 \).

1. \( x = 0 \):
\[
f(0) = -((0) + 1.4)^2 + 6 = -(1.4)^2 + 6 = -1.96 + 6 = 4.04
\]

2. \( x = 1 \):
\[
f(1) = -((1) + 1.4)^2 + 6 = -(2.4)^2 + 6 = -5.76 + 6 = 0.24
\]

3. \( x = 2 \):
\[
f(2) = -((2) + 1.4)^2 + 6 = -(3.4)^2 + 6 = -11.56 + 6 = -5.56
\]

4. \( x = 3 \):
\[
f(3) = -((3) + 1.4)^2 + 6 = -(4.4)^2 + 6 = -19.36 + 6 = -13.36
\]

Now, we can summarize these results in the table:

| x | f(x) |
|-----|----------|
| 0 | 4.04 |
| 1 | 0.24 |
| 2 | -5.56 |
| 3 | -13.36 |

### Summary of Answers:
- **Part A:** Vertex = \( (-1.4, 6) \)
- **Part B:**

| x | f(x) |
|-----|----------|
| 0 | 4.04 |
| 1 | 0.24 |
| 2 | -5.56 |
| 3 | -13.36 |